Worked solution
Juice mixtures: conserve volume and each ingredient
Three brands of apple juice, A, B and C, each contain a certain percentage of pure juice and some artificial flavouring. The breakdown of the amount of juice and flavouring for each brand is summarised in the table below.
| A | B | C | |
|---|---|---|---|
| Pure juice (%) | 20 | 70 | 40 |
| Artificial flavouring (%) | 0.5 | 0.8 | 0.7 |
How many litres of each brand should be mixed to produce 300 litres of juice with 41.1% pure juice and 0.647% artificial flavouring? marks
[2016/ACJC/Promo/1]
CJC · Review Problems · Question 4
Answer
A: 127.5 litres; B: 96 litres; C: 76.5 litres.
Three conservation equations
Let be litres of brands A, B, C. Total volume: . Pure juice: . Artificial flavouring: . Percentages must be divided by 100, including those smaller than 1%.
Solve the amounts
The source GC solution is . Mix 127.5 litres of A, 96 litres of B and 76.5 litres of C. These sum to 300 litres and contain 123.3 litres pure juice and 1.941 litres flavouring, exactly the required percentages.
Common mistakes
0.647% is 0.00647 of the mixture, not 0.647 of it.
Solution notes
Also printed as Review 4 in both CJC Linear Equations lecture copies: question PDF page 14 / printed 174; answer PDF 15 / Student printed 175, Teacher visible footer 15 (extracted 175). Compared in evidence/review-cjc-linear-equations-lecture.md; the repeated asks, tables and marks retain this existing identity.